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Filter Design

I’d like to add another trick to your digital filter toolbox: when you apply any filter in both directions on your input signal, the combined filtering operation is zero phase. As you know from… read more

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Say that you have implemented a low-pass FIR filter with the correct cut-off frequency and transition band, but that you are not quite happy with the suppression of frequencies in the stop band. A straightforward trick to put in your toolbox is that you can double the suppression by… read more

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In my articles on filter design I mostly focus on a rather specific subset of all possible filters, namely symmetrical FIR filters with an odd number of coefficients. Each of these properties (1. FIR, 2. symmetrical, and 3. an odd number of coefficients) was chosen for… read more

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This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. For the specific case of a filter, the frequency response tells you exactly how each frequency is altered. The example code is… read more

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This article explains how to create a windowed-sinc filter with a Kaiser (or Kaiser-Bessel) window. The windowed-sinc filters in previous articles typically had two parameters, the cutoff frequency and the transition bandwidth (or rolloff). With a Kaiser window, there is a third input parameter, the ripple. For the specific case of the Kaiser window, the same… read more

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This article contains more detailed information on setting the transition bandwidth (or roll-off) from How to Create a Simple Low-Pass Filter. That article suggest to use, as the filter length N, an odd number close to 4/b, where b is the required transition bandwidth. This is a good basic rule. However, in… read more

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This article presents spectral reversal, a technique to turn a low-pass filter into a high-pass filter. Spectral reversal is an alternative for spectral inversion, as described in How to Create a Simple High-Pass Filter. Starting from the cutoff frequency… read more

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The low-pass single-pole IIR filter is a very useful tool to have in your DSP toolbox. Its performance in the frequency domain may not be stellar, but it is very computationally efficient. A low-pass single-pole IIR filter has a single design parameter, which is the decay value d. It is customary to define parameters… read more